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AP EAMCET202422 May 2024Evening ShiftMathematicsProperties of TrianglesActual

In ABC , (r₁+r₂ ) cosec ^2 c 2 =

Options

  1. A2 R ^2 C 2
  2. B4 R ^2 C 2
  3. C4 R ^2 C 2
  4. D2 R ^2 C 2

Correct answer

C. 4 R ^2 C 2

Step-by-step solution

aligned & In ABC , ~A + B + C = & r₁+r₂=4 R ~A 2 ~B 2 C 2 +4 R ~A 2 ~B 2 C 2 &= 4 R C 2 [ ~A 2 ~B 2 + A 2 ~B 2 ]=4 R C 2 [ ~A + B 2 ] &= 4 R C 2 [ ( 2 - C 2 ) ]=4 R ^2 C 2 aligned Now, (r₁+r₂ ) cosec ^2 C 2 = 4 R ^2 C 2 ^2 C 2 =4 R ^2 C 2

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